The composition field, \(\overline{c}\)  is
normalized as \(c=\frac{\overline{c}_{a}-\overline{c}}{\overline{c}_{a}-\overline{c}_{b}}\) ,
with local equilibrium states at \(c=0\)  and \(c=1\) . The dimensionless
peak density field, \(\psi \)  is given by \(\psi =\phi \sqrt{\frac{u}{\lambda q_{0}^{4}}}\) .
We set, \(r=\frac{a\Delta T}{\lambda q_{0}^{4}}=-0.2\) , as a constant
such that Eq. REF  always models a stable crystalline-solid
phase for the peak density field [1]}. With \(c=0\) ,
the peak density field in Eq. REF  describes a hexagonal symmetry
with a periodic spacing of \(\frac{4\pi }{q_{0}\sqrt{3}}\)
at equilibrium. Note, \(\frac{1}{q_{0}}\)  is the length scale of the
PFC model and \(\vec{x}=q_{0}\vec{r}\) . The gradient energy coefficient
\(\kappa =\frac{F_{0}}{(\overline{c}_{a}-\overline{c}_{b})^{2}}\left(\frac{16\pi }{q_{0}\sqrt{3}}\right)^{2}\) ,
is numerically calibrated such that the width of the diffuse composition
interface spans over \(\sim 4\)  peaks described by the peak density
field, \(\psi \) . We introduce a constant, \(\gamma =\frac{\lambda ^{2}q_{0}^{5}}{uF_{0}}\) 
that relates the free energy normalizations of the Cahn-Hilliard and
the PFC model. For simulations in this paper, we set \(\gamma =1\) . 
